Question

Select the new equation formed after collecting all variables on one side of the equal sign. (There is more than 1 correct answer.)

1/2(6x + 8) = x − 8


Responses

4 = -2x - 8
4 = -2x - 8

3x = x -12
3x = x -12

8 = -2x - 8
8 = -2x - 8

2x + 4 = -8
2x + 4 = -8

3x + 12 = x
3x + 12 = x

2x + 8 = 8

Answer 1

To collect all variables on one side of the equation \( \frac{1}{2}(6x + 8) = x - 8 \), let's first simplify the left-hand side:

1. Distribute \( \frac{1}{2} \):
\[
\frac{1}{2}(6x + 8) = 3x + 4
\]

Now we have the equation:
\[
3x + 4 = x - 8
\]

Next, we will rearrange it by moving all terms involving \( x \) to one side and all constant terms to the other side. We can do this in different ways:

1. Subtract \( x \) from both sides:
\[
3x - x + 4 = -8
\]
This simplifies to:
\[
2x + 4 = -8
\]
**(Correct Answer)**

2. Subtract \( 4 \) from both sides:
\[
3x + 4 - 4 = x - 8 - 4
\]
This simplifies to:
\[
3x = x - 12
\]
**(Correct Answer)**

3. Subtract \( 4 \) from both sides and then increase both sides by \( 8 \):
\[
3x + 4 - 4 + 8 = x - 8 + 8
\]
This simplifies to:
\[
3x + 12 = x
\]
**(Correct Answer)**

4. Rearranging the equation can also lead us to:
\[
3x + 4 + 8 = x
\]
This simplifies to:
\[
8 = -2x - 8
\]
**(Correct Answer, if we apply a different approach)**

From your responses, the correct answers after rearranging would be:

- \( 2x + 4 = -8 \)
- \( 3x = x - 12 \)
- \( 3x + 12 = x \)

So the correct answers based on these steps are:
1. \( 2x + 4 = -8 \)
2. \( 3x = x - 12 \)
3. \( 3x + 12 = x \)

Note: The other responses provided (like \( 4 = -2x - 8 \) and \( 8 = -2x - 8 \)) do not appear to be in a consistent arrangement based on the starting equation.